Question

12.4. Measure of Dispersion2076 Q.No. 15 Find the standard deviation of: 4, 6, 8, 10, 12.​

Answer 1

Answer:

Standard deviation of given data = 3.16227

Step-by-step explanation:

Step(i):-

Given sample size 'n' = 5

Given data  4, 6,8,10,12

$Mean = \frac{4+6+8+10+12}{5} = 8$

Mean of the sample x⁻ = 8

Standard deviation of the sample

                  $S.D = \sqrt{\frac{Sum(x-x^{-} )^{2} }{n-1}}$

Step(ii):-

Given data

x          :         4      6       8       10      12

x-x⁻      :      4 - 8   6-8   8-8    10-8    12-8

(x-x⁻)   :        -4      -2     0          2        4

(x-x⁻)²  :        16     4       0         4        16  

 

  $S.D = \sqrt{\frac{Sum(x-x^{-} )^{2} }{n-1}}$

  $S.D = \sqrt{\frac{16+4+0+4+16}{4}}$

 S.D = √10 = 3.16227

Final answer:-

The standard deviation = 3.16227